SIMULATION OF THE GROUND VIBRATION INDUCED BY TRAIN

Abstract

The purpose of this study is to make clear the mechanism of the ground vibration induced by trains and to develop a numerical simulation tool which can quantitatively evaluate the effect of wave filtering works. A 3D viscoelastic finite-difference method is used to study the mechanism of the ground vibration induced by train. At first, the special case which the force from train is constant for place is analyzed, because the ground vibration does not happen in this case. So the not-constant force from the train is measured. Finally, a numerical simulation is promoted by using this inhomogeneous force from the train. The result of this numerical simulation qualitatively and quantitatively resembles field ground vibration data. It is recognized that one reason of the generation of the ground vibration is caused by inhomogeneous force from the train. Introduction Running trains generate ground vibration and can require attenuation methods to be engineered to reduce problems for people and structures near the track. In the case of the Shinkansen ‘bullet-trains’ in Japan, their source characteristics have not been investigated in detail. Thus, the transient force from the train onto the tracks is measured by using strain gauges mounted on the wheels, and conducted 3D numerical wavefield simulations employing these sources forces. In the second section, methodology of the 3D finite-difference numerical simulation is outlined. A 3D viscoelastic finite-difference method is used to adjust the attenuation. In the third section, qualitative classification of source characteristics is tested specially. Because on the homogeneous medium, a kind of ideal static line source dose not induce the vibrational response (Dunkin and Corbin, 1970). Finally, a quantitative simulation is promoted. 409 Methodology of the 3D finite-difference numerical simulation With the previously estimated input waveform, the wavefield propagating through an earth model can be calculated by numerical simulation. We use the viscoelastic wave equation (Robertsson et al, 1994) and a 3D Finite Difference method (FD). The grid arrangement of the FD framework is a standard staggered grid. The absorbing boundaries at the sides and bottom are based on Cerjan et al (1985). At the top of the grid (free surface) two boundary conditions are employed. Along the train tracks, the stress is set to zero, as per Levander et al (1988). Elsewhere at the surface, both primary wave velocity Vp and secondary wave velocity Vs are set to zero, known as the vacuum formulation (Graves, 1996). Referring to Blanch et al (1995) and using the Zener model, the attenuation factor Q is dominated by ( ) ( ) 2 0 0 1 0 0 1 / Q I Q I ω ω ω ω ω + = (1) Where, ( ) { } 2 0 0 0 ln 1 / 2 b a I ω ω ω ω ω ⎡ ⎤ = + ⎣ ⎦ , ( ) ( ) 0 0 1 0 2 0 / arctan / 2 1 / b